Transient behaviour of a suction caisson in sand: axisymmetric numerical modelling

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Transient behaviour of a suction caisson in sand:

axisymmetric numerical modelling

B. Cerfontaine, F. Collin and R. Charlier

University of Liege, Belgium

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Outline

1 Context

2 Description of the case study

3 _Results

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Table of contents

1 Context

2 _{Description of the case study}

3 Results

Reaction modes Monotonic simulations Cyclic simulations

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Context

Motivations

1 EU 2020 objectives (greenhouse gas, renewable energy, energy

efficiency)

2 Basic working of soil-caisson system upon both monotonic and cyclic

loading (serviceability)

3 Highlighting of components of reaction : first step to the elaboration

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Context

Motivations

efficiency)

3 Highlighting of components of reaction : first step to the elaboration

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Motivations

efficiency)

3 Identifications of components of reaction : first step to the

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Suction caissons for offshore foundations Houlsby et al. (2005) Pumping Water flows Decreasing inside pressure

Offshore wind turbines specificities light structure

high overturning moment Suction caissons specificities

hollow steel cylinder open towards the bottom

extensively used as anchors in the North Sea

monopod or tetra/tri-pod superstructure

cheaply and quickly installed, reusable, Senders (2008)

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Table of contents

1 Context

3 Results

Reaction modes Monotonic simulations Cyclic simulations

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Geometry

Seabed

Sea level Waves + Wind

Published in Cerfontaine et al.

(2016), G´eotechnique Modelling (axisymmetric) Lid Elastic superficial layer Inner interface (top) Outer interface (skirt) Inner interface (skirt) Skirt Elastic toe Height (H ) Radius (D/2)

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Geometry

Seabed

(2016), G´eotechnique Modelling (axisymmetric) Initial stress (interface) Height (H ) Radius (D/2) Loading Initial stress (soil)

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Geometry

Seabed

(2016), G´eotechnique

Size

D=7.8m and H=4m Soil-steel friction coefficient

µ = 0.5 Permeability

k= 5 · 10−12m2

Coefficient of lateral earth pressure at rest

K0= 1.0

Porosity

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Prevost model for cohesionless soils - Kinematic hardening

After Elgamal (2003)

Implementation in LAGAMINE code published in Cerfontaine et al. (2014) NUMGE2014 Proceedings

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Prevost model for cohesionless soils - Volumetric behaviour p' q Contractive Dilative PT line Current stress state Trace of current yield surface η

Non-associated plastic volumetric behaviour ˙p_v = 1 3 · η2− ¯η2 η2_{+ ¯}_η2 · ˙λ η = q/p0

˙λ continuous plastic multiplier ¯

η phase transformation ratio, Ishihara (1975)

Very simple (only 1 param.) ⇒ satisfactory to a 1st approx.

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Cyclic triaxial tests (Lund Sand, Dr= 90%, Ibsen & Jakobsen (1996))

Two distinct behaviours from two initial deviatoric stress invariants

0 10 20 30 40 50 60 70 80 −20 −10 0 10 20 30 40 50 60 70 p’ [kPa] q [kP a] PT Line 0 10 20 30 40 50 60 70 80 −20 −10 0 10 20 30 40 50 60 70 p’ [kPa] q [kP a] PT Line

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Hydro-mechanically coupled interface element Mechanical behaviour |tT| p' f>0 f<0 f=0 Elastic domain Plastic surface No contact µ N + Penalty method Flow behaviour Side 2 Side 1 Inside gN fwt2 fwt1 fwl Couplings

Effective stress Storage Permeability

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Table of contents

1 Context

3 Results

Reaction modes

Monotonic simulations Cyclic simulations

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Reaction of the caisson to applied vertical load ΔFtot ΔFin ΔFout ΔFtop ΔFtip ΔFpw ΔFtot

Resistance to compressive load ∆Ftot

∆Fin, inner friction ;

∆Fout, outer friction ;

∆Fpw, pore water pressure

(> 0) ;

∆Ftop, top effective stress ;

∆Ftip, tip effective stress.

ΔFtot ΔFtot

ΔFin ΔFout

ΔFpw

Resistance to extension load ∆Ftot

∆Fin, inner friction ;

∆Fout, outer friction ;

∆Fpw, pore water pressure

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Table of contents

1 Context

3 Results

Reaction modes

Monotonic simulations

Cyclic simulations

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Monotonic extension simulations (load controlled) Drained −3 −2.5 −2 −1.5 −1 −0.5 0 −3 −2.5 −2 −1.5 −1 −0.5 0 ∆ y [mm] ∆ F [MN] ∆ Ftot ∆ F_in ∆ F_out ∆ F_lid ∆ F_tip Upwards

Partially drained (8kPa/s)

−3 −2.5 −2 −1.5 −1 −0.5 0 −3 −2.5 −2 −1.5 −1 −0.5 0 ∆ y [mm] ∆ F [MN] ∆ F_tot ∆ F_in ∆ F_out ∆ F_lid ∆ F_tip ∆ F_pw Upwards

∆Fin and ∆Fout bounded

∆Fin< ∆Fout (unloading)

∆Fin and ∆Fout bounded

∆Fin< ∆Fout (unloading)

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Pore water pressure generation during extension -2.80 -5.70 -8.60 -11.5 -14.4 -17.3 -20.2 -23.1 -26.0 -28.9 -31.8 -34.7 Δpw [kPa] Pload = 55.5kPa

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Table of contents

1 Context

3 Results

Reaction modes Monotonic simulations

Cyclic simulations

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Results Cyclic simulations

Pseudo-random and equivalent loadings

0.8 0.85 0.9 0.95 1 −10 0 10 20 30 40 50 60 70 Time[h] Plo ad [kP a] Extreme event 0 0.5 1 1.5 2 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 Time [h] Fy /m ax(| Fy |) [− ] Extreme event Short Signal ΔPload=45kPa Pload,av=20kPa

Batch 1 Batch 2 Batch 3 Batch 4

Nb. cycles [-] 50 28 4 1

T [s] 4.6 11 11.6 11.1

∆P [kPa] 4.5 13.5 22.5 40.5

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Results Cyclic simulations

Pseudo-random and equivalent loadings

0.8 0.85 0.9 0.95 1 −10 0 10 20 30 40 50 60 70 Time[h] Plo ad [kP a] Extreme event 0 0.5 1 1.5 2 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 Time [h] Fy /m ax(| Fy |) [− ] Extreme event Short Signal ΔPload=45kPa Pload,av=20kPa Nb. cycles [-] 50 28 4 1 T [s] 4.6 11 11.6 11.1 ∆P [kPa] 4.5 13.5 22.5 40.5 Time Time Pload,mean Pseudo-Random Equivalent ΔT1 ΔP1 ΔP2 ΔP3 ΔP1 ΔP2 ΔP3 ΔT1 Pload Pload,mean Pload Half-cycle analysis

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Pseudo-random and equivalent loadings 0.8 0.85 0.9 0.95 1 −10 0 10 20 30 40 50 60 70 Time[h] Plo ad [kP a] Extreme event 0 0.5 1 1.5 2 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 Time [h] Fy /m ax(| Fy |) [− ] Extreme event Short Signal ΔPload=45kPa Pload,av=20kPa

Batch 1 Batch 2 Batch 3 Batch 4

Nb. cycles [-] 50 28 4 1 T [s] 4.6 11 11.6 11.1 ∆P [kPa] 4.5 13.5 22.5 40.5 Time Time Pload,mean Pseudo-Random Equivalent ΔT1 ΔP1 ΔP2 ΔP3 ΔP1 ΔP2 ΔP3 ΔT1 Pload Pload,mean Pload Half-cycle analysis

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Pseudo-random and equivalent loadings 0 100 200 300 400 500 600 -20 0 20 40 60 80 Pload [k Pa ] Pload [k Pa ] Pseudo-random Equivalent 1 Equivalent 2 Equivalent 3 Time [s] Time [s] Time [s] Time [s] Pload [k Pa ] Pload [k Pa ] 0 100 200 300 400 500 600 -20 0 20 40 60 80 0 100 200 300 400 500 600 -20 0 20 40 60 80 0 100 200 300 400 500 600 -20 0 20 40 60 80

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Cyclic partially drained behaviour 0 100 200 300 400 500 600 −40 −20 0 20 40 Time [s] ∆p [kPa] ∆p_w ∆p_tot 0 100 200 300 400 500 600 −40 −20 0 20 40 Time [s] ∆p [kPa] Envelope curves Tendency Envelope curves Tendency Envelope curves ∆p_w,p2p Envelope curves

Envelope and tendency curves : permanent and transient

Loading mainly sustained by pore water pressure (PWP) Accumulation of PWP (max 5kPa)

Highest accumulation during extreme event

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Cyclic partially drained behaviour : displacement and PWP accumulation 0 200 400 600 800 1000 −1 0 1 2 3 4 5 6 7 8 Time [s] ∆ pw [kPa] Equiv.1 Equiv.2 Equiv.3 Random Consolidation 0 200 400 600 800 1000 0.5 1 1.5 2 2.5 3 3.5 ∆ y [mm] Time [s] Equiv.1 Equiv.2 Equiv.3 Random Consolidation Maxima

Max PWP (extreme event sooner)

Lowest PWP (random)

Almost no effect of small cycles

Linear and non-linear parts High accumulation for extreme event

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Cyclic partially drained behaviour : influence of permeability 0 500 1000 1500 2000 0.5 1 1.5 2 2.5 3 3.5 Time [s] ∆ y [mm] 5*10−13 5*10−12 5*10−11 5*10−10 k [m2] Consolidation End −5 0 5 10 0 5 10 15 20 25 q [kPa] p’ [kPa] 5*10−13 5*10−12 5*10−11 5*10−10 k [m2] A B₋₁₂ B₋₁₁ B₋₁₀ B₋₁₃ Failure PT line

No linear trend with permeability evolution Local failure for the highest permeability (high effective

Different stress paths under the lid centre with permeability

Decrease of p0 due to PWP

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Table of contents

1 Context

2 Description of the case study

3 _Results

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Conclusions and perspectives

Coupled modelling of a suction caisson upon monotonic and cyclic loading

Importance of the partially drained behaviour (both monotonic and cyclic)

Identification of different modes of resistance not activated all at the same time

Complex behaviour and accumulation of settlement during a short-time storm event

Perspectives

Calibration procedure and validation of the model Elaboration of a macro-element

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Coupled modelling of a suction caisson upon monotonic and cyclic loading

Importance of the partially drained behaviour (both monotonic and cyclic)

Identification of different modes of resistance not activated all at the same time

Complex behaviour and accumulation of settlement during a short-time storm event

Perspectives

Calibration procedure and validation of the model Elaboration of a macro-element

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References

Houlsby, G. T., Ibsen, L. B. & Byrne, B. W. (2005). Suction Caissons for Wind Turbines. International Symposium on Frontiers in Offshore Geotechnics, 75(September), 94.

Senders, M. (2008). Suction caissons in sand as tripod foundations for offshore wind turbines. PhD Thesis, University of western Australia.

Elgamal, A., Yang, Z., Parra, E. & Ragheb, A. (2003). Modeling of cyclic mobility in saturated cohesionless soils. International Journal of Plasticity, 19(6), 883-905.

Ishihara, K., Tatsuoka, F. & Yasuda, S. (1975). Undrained Deformation and liquefaction of sands under cyclic stresses. Soils and Foundations, 15(1), 29 ?44.

Cerfontaine, B., Collin, F. & Charlier, R. (2016). Numerical modelling of transient cyclic vertical loading of suction caissons in sand. G´eotechnique, 66(2), 1-16.

Cerfontaine B. & Charlier, R. (2014) Implicit implementation of the Prevost model. Proceedings of the eight European Conference in Numerical Methods in Geotechnical Engineering.

Ibsen, L.B. & Jacobsen, F.R. (1996) Lund sand no.0. Technical report, Aalborg University. Cerfontaine (2014) The cyclic behaivour of sand, from the Prevost model to offshore geotechnics. PhD Thesis, University of Li`ege.

Cerfontaine, B., Dieudonn´e, A. C., Radu, J. P., Collin, F., & Charlier, R. (2015). 3D zero-thickness coupled interface finite element : Formulation and application. Computers and Geotechnics, 69, 124-140.